Measurement of the branching fraction for $\ddot{I}ˆ(3686)\to \ddot{I}‰K^{+}{K}^{-}$

Abstract

With $1.06\times 10^8$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, the branching fraction of $\ddot{I}ˆ(3686)\to \ddot{I}‰K^{+}{K}^{-}$ is measured to be $(1.54\pm 0.04\pm 0.11)\times 10^{-4}$. This is the most precise result to date, due to the largest $\ddot{I}ˆ(3686)$ sample, improved signal reconstruction efficiency, good simulation of the detector performance, and a more accurate knowledge of the continuum contribution. Using the branching fraction of $J/\ddot{I}ˆ\to \ddot{I}‰K^{+}{K}^{-}$, the ratio $\mathcal{B}(\ddot{I}ˆ(3868)\to K^{+}{K}^{-})/\mathcal{B}(J/\ddot{I}ˆ\to K^{+}{K}^{-})$ is determined to be $(18.4\pm 3.7)\%$. This constitutes a significantly improved test of the $12\%$ rule, with the uncertainty now dominated by the $J/\ddot{I}ˆ$ branching fraction.